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What I Used To Know Isn’t Good Enough

By • September 16, 2009 • 11 Comments

One of my most vivid memories of childhood is carpooling with Brad’s mom to a church group when I was ten. It was early fall and we were talking about the changing seasons when she quoted her husband, an amateur astronomer: “We’re losing a minute of sunlight every day.”

That remark was so traumatizing that even now, almost twenty years later, I can recall the exact cross-street we passed when she said it.

I pictured neverending darkness. Riots. I wondered if we should maybe skip church group and stock up on flashlight batteries before the rest of town found out. Even at that age, my sense of patterns (and what a math teacher years later would call “indirect variation”) was developed enough to understand that we didn’t have much time left.

This is what I used to know:

.

That was a perfect, teachable moment for someone to step in and show me that what I used to know wasn’t good enough. “Not everything works like a line. Some things work like a cycle, getting bigger, getting smaller, getting bigger again. Can you think of anything else that works like a cycle?” Et cetera.

It has taken me six years to rewire my teaching to approach new knowledge as the solution to the limitations of what we used to know, rather than as an entry on a list of standards or “what we’re learning today.”

Related:

  1. The First Day Of Summer School.

Excellent Math Blogging

By • September 14, 2009 • 5 Comments

These two are fresh. If you subscribe now, you can say you were into them before they got big.

1.

Tony Alteparmakian is a 2009 Leader in Learning enacting Chris Lehmann’s vision of classroom inversion (though I don’t doubt they came to the idea separately). Their idea is that we should send our students home with what used to constitute classroom time โ€“ the lecture โ€“ and spend classroom time on labs and teacher-led enrichment of that material.

Obviously, that vision comes fully loaded with complications but Tony is resolving them one-by-one in a how-to series that has only just started.

Also, I dig his redesigns. It’s hard to argue with slide transformations like these.

Before:

After:

2.

Sean Sweeney is an extra-value meal. In one corner of the edublogosphere you have the edtechnologists, the district IT staff, the ICT professionals, the policy wonks, etc., all asking huge, important questions about merit pay, technology integration, assessment, online schooling, etc., and posing reckless hypotheticals about limitless resources with nothing less than the future of education at stake, and all of it makes me grateful for guys like Sean who are driving 90MPH up the right lane, offering educators something they can use in the classroom right. now.

I’m talking about his quadratic catapult project. Or his Graphing Stories remix. Or his exercise in grocery store estimation. And that’s his output over two weeks.

This is math-instruction-as-artistic-expression and it’s cool as hell to watch.

“A Trash-Talking High School Math Teacher”

By • September 12, 2009 • 16 Comments

The story broke online: the express lane isn’t faster. Jaws hit the floor. It made a few laps around the blogosphere while the MSM played catch-up. 72 hours later, I was in front of a camera, explaining the regression to a reporter for CBS in San Jose who in turn challenged me to a race down the checkout lines.

Here is that (two-minute) clip:

Click through to view embedded content.

Three takeaways:

  1. Slow news night.
  2. Everyone has an opinion on this one. Most people also have a demographic they are particularly loathe to find ahead of them in line.
  3. This visceral, widespread reaction to nothing more than a) a clear picture, and b) a concise question will do nothing to make my WCYDWT evangelism less insufferable. Apologies in advance. This isn’t the only way to teach, but it is a fun way.

What I Would Do With This: Groceries

By • September 8, 2009 • 159 Comments

[following up from here]

All other things being equal, which lane is the fastest?

This problem has obsessed me for years. It’s my DaVinci code. It’s my love for math, for mathematical reasoning, for the relentless deconstruction of something that seems simply intuitive into data, models, and computation.

This is also my love for WCYDWT media.

Perfunctory Pitch For WCYDWT Math Instruction

You have here a simple question that anyone can access. Doesn’t matter that you’ve never run a linear regression in your life. If you’ve ever shopped for groceries, if you’ve ever stood in line with a candy bar, a soda bottle, and a matinee starting across town in ten minutes, you have an opinion here. And I can use that.

The question is simple and so is the answer but the justification is extremely complicated, which is exactly how I’d like to balance the learning experience. We will argue. There are easily a dozen variables affecting the line speed that have nothing to do with the number of customers in each line or the number of items in their baskets. You could assign some field research here. I spent ninety minutes last week just watching, counting, and timing groceries as they slid across a scanner.

The question is also scalable. We can remix this single image into endlessly difficult scenarios (or easier scenarios) that will push a student’s hypothesis to the crumbling point and back again.

A (Broad) Lesson Plan

Gather the data. Or supply the data. Graph the data. Develop a model. Test the model. Talk about the effect of outliers. Assign weight to outlying variables.

I threw some questions on a worksheet five years ago, fairly predictable stuff like “what does it mean when a point is above the line of best fit?” At this point, though, I’m hesitant to constrain the activity even that lightly. I’d almost rather pick a fight with a student who finished early and let the rising pitch of that conversation fold in a few more learners.

Other Remarks

  1. Check is slower than credit which is slower than cash. Students are sometimes surprised that cash is faster than credit. From my observations, the fastest cash transaction will outpace the fastest credit transaction by a wide margin but there is also huge variance in credit transactions. I mean, some people have absolutely no idea what they are doing with that thing. The same can’t really be said of cash.
  2. The store manager hooked up some checkout data, which was awesome. At first, he declined my request for numbers while agreeing to let me float around the store. Then he brought back the mother lode: checkout scanner data from a single six-hour shift. The data was aggregated in a few unhelpful ways but no way do I mind this particular excerpt, which gives away the store:
  3. The y-intercept is non-zero! This never fails to trip my fuses. It should take you zero seconds to purchase zero items but you can’t ignore the fixed time cost of the pleasantries (“Hi. How are you doing? Do you need any help out?”) and the transaction itself.
  4. The express lane isn’t faster. The manager backed me up on this one. You attract more people holding fewer total items, but as the data shows above, when you add one person to the line, you’re adding 48 extra seconds to the line length (that’s “tender time” added to “other time”) without even considering the items in her cart. Meanwhile, an extra item only costs you an extra 2.8 seconds. Therefore, you’d rather add 17 more items to the line than one extra person! I can’t believe I’m dropping exclamation points in an essay on grocery shopping but that’s how this stuff makes me feel.

Here’s the Photoshop template, which you’re welcome to remix with new numbers or, even better, revamp into something altogether less offensive to the eye.

[BTW: check out this fun snap from Dan Callahan of the Whole Foods staff bulletin board.

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